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Decomposition of water and fat in magnetic resonance imaging (MRI) is important for biomedical research and clinical applications. In this paper, we propose a two-phased approach for the three-point water-fat decomposition problem. Our contribution consists of two components: 1) a background-masked Markov random field (MRF) energy model to formulate the local smoothness of field inhomogeneity; 2) a new iterated conditional modes (ICM) algorithm accounting for high-performance optimization of the MRF energy model. The MRF energy model is integrated with background masking to prevent error propagation of background estimates as well as improve efficiency. The central component of our new ICM algorithm is the stability tracking (ST) mechanism intended to dynamically track iterative stability on pixels so that computation per iteration is performed only on instable pixels. The ST mechanism significantly improves the efficiency of ICM. We also develop a median-based initialization algorithm to provide good initial guesses for ICM iterations, and an adaptive gradient-based scheme for parametric configuration of the MRF model. We evaluate the robust of our approach with high-resolution mouse datasets acquired from 7T MRI.